How to model a round chair?
I'll answer regarding the white/orange chair.

The outer spherical shell and the base are easy enough to model. You can start with a sphere and use the Solidify modifier to give it thickness. If you rotate the sphere you can simply cut out part of the sphere to get the opening. The base can be simply modelled by extruding a circle.

The more difficult part is the cushion. I would start by box modelling the approximate shape and position of the cushion and the sculpt it into the final shape and position. You can see the cushion gently hugs the opening of the chair so that would need to be modelled/sculpted into place.